A forced rectangle is the only rectangle a number can still form. Every other option would cross the grid edge, contain a second number, or overlap a rectangle you have already drawn — so you can draw it with certainty.
What “forced” means
Each number starts with a list of possible rectangles. Solving Shikaku means shrinking those lists. When a list has one entry, the number is forced.
The three blockers
- The border — see corners and edges.
- Other numbers — a rectangle can never contain two numbers.
- Placed rectangles and claimed cells — anything already decided is off-limits.
Forced from the start
Some numbers are forced before you draw anything. In this generated 6×6 puzzle:
Forced later
Most forced rectangles appear only after earlier moves shrink the space. Here a number that began with several options is pinned down by its neighbours:
A scanning routine
- After every rectangle you draw, re-check the numbers that touch it.
- Numbers whose options all overlap the new rectangle except one are now forced.
- Repeat until nothing changes, then switch to unreachable cells or overlap.
Practise on this puzzle
The example above comes from this 6×6 easy grid.
Questions
What is a forced move in Shikaku?
A number with exactly one remaining legal rectangle. Drawing it is always correct.
What should I do when no rectangle is forced?
Look for cells only one number can reach, then for cells shared by every option of a number (overlap).